An Examination of the Effects of Aerosol Chemical Composition and Size on Radiative Properties of Multi-Component Aerosols

The sensitivity of aerosol radiative properties (i.e., scattering coefficient, extinction coefficient, single scatter albedo, and asymmetry factor) and radiation transmission to aerosol composition, size distributions, and relative humidity (RH) is examined in this paper. Mie calculations and radiation calculations using a tropospheric visible radiation model are performed. The aerosol systems considered include inorganic and organic ions (e.g., Cl-, Br-, 3 NO , , Na , 4 SO  4 NH  , K, Ca, Mg, HCOO-, CH3COO-, CH3CH2COO-, CH3COCOO-, OOCCOO2-, MSA1-), and water-insoluble inorganic and organic compounds e.g., (black carbon, n-alkanes, SiO2, Al2O3, Fe2O3 and other organic compounds). The partial molar refraction method and the volume-average method are used to calculate the real and imaginary parts of refractive index of real aerosols, respectively. The sensitivity simulations show that extinction coefficient increases by 70% when RH varies from 0 to 80%. Both extinction coefficient and asymmetry factor increase by ~48% when real part varies from 1.40 to 1.65. Scattering coefficient and single scattering albedo decrease by 18% and 24%, respectively, when the imaginary part varies from –0.005 to –0.1. Scattering and extinction coefficients increase by factors of 118 and 123, respectively, when the geometric mean radius varies from 0.05 to 0.3 m. Scattering and extinction coefficients and asymmetry factor increase by factors of 389, 334, and 5.4, respectively, when geometric standard deviation varies from 1.2 to 3.0. The sensitivity simulations using a tropospheric visible radiation model show that the radiation transmission is very sensitive to the change in geometric mean radius and standard deviation; other factors are insignificant.


Introduction
Atmospheric aerosols may influence the Earth's radiation balance directly by backscattering and absorption of solar radiation, and indirectly by increasing cloud condensation nuclei (CCN) concentrations, which in turn increase cloud droplet concentrations and thus backscattering of solar radiation [1][2][3].The IPCC [4] concluded that increasing concentrations of the long-lived greenhouse gases have led to a combined radiative forcing +2.63 [± 0.26] W  m -2 , and the total direct aerosol radiative forcing is estimated to be -0.5 [± 0.4] W m -2 , with a medium-low level of scientific understanding, while the radiative forcing due to the cloud albedo effect (also referred to as the first indirect effect), is estimated to be -0.7 [-1.1, +0.4] W   m -2 , with a low level of scientific understanding.Evaluation of aerosol direct radiative forcing is complicated by the fact that aerosols are highly and non-uniformly distributed over the Earth and comprise a variety of chemical species, and their abundance varies with particle size, location and time.As indicated by Penner et al. [5], one of central scientific questions related to the direct radiative influence of aerosols is how the aerosol composition and size distributions affect the optical depth and radiative properties of aerosols, including dependence on relative humidity.Up to today the sensitivity of direct aerosol forcing to chemical composition, size distribution and relative humidity on a global scale has been tested with a "reference box model" [1] and a GCM model [6][7][8] Most of these studies except for Jacobson (2001) on direct aerosol forcing only focused on anthropogenic sulfate aerosols.The objectives of this paper are (1) to accurately calculate the refractive index of aerosol particles with the known chemical composition of atmospheric aerosol; (2) to theoretically evaluate the sensitivity of aerosol radiative properties and radiation transmission in the visible range to refractive index, size distributions, and relative humidity (RH) using a box model that includes Mie and radiative transfer calculation.Since the aerosol particle refractive index is determined by its chemical composition, the dependence of radiative properties of aerosol particles on the refractive index can indicate the effects of chemical composition.Since most of the light scattering and extinction are caused by particles in the accumulation mode size range (0.1 -1.0 m, diameter), and these particles are neither removed effectively by impaction nor by diffusion, the accumulation mode particles are the most important one in terms of aerosol radiative forcing.In this study the sensitivity of aerosol radiative properties to size distribution is examined on the basis of the calculation of the particle radiative properties for the accumulation mode only.

Atmospheric Aerosol Composition and Size Distribution
Atmospheric aerosol particles are composed of complex mixtures of natural and anthropogenic chemical species that include (1) water-soluble inorganic and organic compounds such as sulfate, nitrate, formate and acetate, (2) water-insoluble inorganic and organic compounds such as black carbon, Al 2 O 3 and n-alkanes, and (3) water itself.Soluble individual anion and cation concentrations of atmospheric aerosol are typically measured by Ion Chromatography (IC), and elements such as Al and Pb are determined by partially induced X ray emission (PIXE).On the other hand, the concentrations of insoluble high molecular weight organic compounds in aerosols are measured by gas-chromatography-masss pectrometer (GS/MS) method [9].The IC and PIXE methods provide no information on the concentrations of specific salts or classes of inorganic and organic salts.The GC/MS method can quantify the concentrations of individual organic compounds in atmospheric particles.However, only about 10% of the total organic mass can be typically identified by the GC/MS method [9.In general, the water-soluble materials within atmospheric aerosol particles are expected to be a mixture of different chemicals and the water soluble parts of aerosol particles are considered to be a mixture of electrolytes together with any other water-soluble material.There are possible interactions between those ions that do not commonly exist between chemical components, especially at high RH conditions [10].For example, in a mixture of KNO 3 and NaCl, there is a possible interaction between K + and Na + .It is therefore reasonable to consider water-soluble parts of aerosol particles as a mixed solute, and aerosol particles at a dry state composed of mixed solute and insoluble substances.Since the composition of the aerosol particles depends on the sources and subsequent transformation while airborne, it is possible to separate aerosols into urban, rural continental and marine aerosols in a first approximation [11].SO  , Na + , 4 NH  , K + , Ca 2+ , Mg 2+ , SiO 2 , Al 2 O 3 , and Fe 2 O 3 ), total concentrations of organics, and total mass concentrations of aerosol particles for three aerosol types were taken from the estimates of Pueschel [11].For organics, over 80 individual organic compounds found in aerosol particles were identified and quantified previously [9].In this study, the concentrations of soluble organic compounds (HCOO -, CH 3 COO -, CH 3 CH 2 COO -, CH 3 COCOO -, 2 CCOO OO  , Methane sulfonic acid (MSA)) were taken from the estimates of Yu [2].Chylek et al. [12] showed that the average black carbon (BC) atmospheric concentration in the continental air was 0.23 ± 0.04 g/m 3 compared with 0.03 ± 0.01 g/m 3 for the maritime air in the measurements over the southern Nova Scotia.Huntzicker et al. [13] indicated that the average BC concentration for 26 cities in the United State was 3.8 g/m 3 .In this study, the BC concentrations used for urban, continental, and marine aerosols are 3.8, 0.23 and 0.06 g/m 3 , respectively.The other organic compound concentrations listed in Table 1 were taken from the estimates of Roggie et al. [9].Table 2 lists the physical chemical and optical properties of various pure salts in atmospheric particles.For the aerosol model computation, a lognormal distribution function is suitable to characterize the size distribution of atmospheric aerosols [11].Particles in the accumulation mode (0.1 -1.0 m, aerodynamic diameter) are the most important one in terms of aerosol radiative forcing.Table 3 lists the typical size distributions for three types of aerosol for the accumulation mode at a dry state compiled from literatures.As shown, the total number concentration, the geometric mean diameter (D g ), and the geometric standard devia-

The Effect of Relative Humidity
Table 2 lists the RH at which the deliquescence will occur for some pure salts (RHD).The effects of continu-ously increasing RH on the growth of a pure salt aerosol particle can be calculated from equilibrium thermodynamics [10].However, it is very difficult to predict this so-called "hysteresis effects" of water uptake for actual multi-component aerosol particles because this not only depends on the history of RH but also varies from one sample to another [10].Here, the particle hysteresis effects should not be considered in detail.Instead, the den- sity, refractive index, and radius of aerosol particles are considered as a unique function of RH in which the "hysteresis effects" are partially taken into account for three aerosol types using the experimental data of Hänel [10]:     where the subscript "w" denotes pure water and "0" indicates the dry substance, m r and m i are the real and imaginary parts of refractive index. is mean linear mass increase coefficient.Figure 1 shows  as a function of RH for three aerosol types, which are obtained from the experimental results in Table 4 of Hänel [10].
As shown, the dependence of  on RH for difference types of aerosols is rather complicated.RH can affect radiative properties of aerosol particles through changing particle size and refractive index.Figure 2 shows the changes of densities, refractive indices, and radius for three type aerosols as a function of RH.As shown, the RH effect is important at RH > 80% for density and refractive index, but the radius is sensitive to the change in RH only when RH > 90%.

Refractive Index Calculation
One of central questions for prediction of radiative properties of aerosol particles is to accurately calculate their refractive indices.As shown in Table 1, the available information on the particle compositions is the ion concentrations of soluble components and compound concentrations of insoluble components.It has been shown that the partial molar refraction approach is applicable to calculate refractive indices for ionic solid-aqueous electrolyte mixtures [14].The partial molar refraction R where n is refractive index, M is molecular weight, and ).If the molar refractions of components are known, the mean refractive index of a medium can be calculated as follows [15]: for an aerosol particle: where R i is the partial molar refraction of component i in , and [AV] is the aerosol volume in 3 g m    .The aerosol volume can be either measured or predicted by:   where  i is the density of component i in g cm -3 .Table 4 lists the partial molar refractions for ions.Table 2 contains the refractive index and density for possible salts found in atmospheric aerosol particles.The refractive index and density for most compounds in aerosol particles range from 1.332 to 2.654 and from 0.783 to 11.344 , respectively.Volz [16] reported densities of water-soluble materials from different rainfalls and locations to be in a range of 1.76 -1.96 . In this study, the average value (1.86 ) is used as the mean density for water-soluble parts in aerosol particles.The density (1.40 ) and refractive index (1.55)for other organic compounds in Table 2 were taken from the estimates of Sloane [17].Additionally, the mean aerosol density, , can be calculated from: In this study, the above partial molar refraction approach is extended to calculate the refractive index of any atmospheric particles with the known chemical compositions.Table 4 lists the partial molar refraction for other aerosol components including insoluble inorganic and organic compounds, which were calculated based on the method of Weast [15].In this study, an internal mixture is assumed for atmospheric aerosol components.Tang [16] showed that both internal and external mixtures exhibited similar light-scattering properties.Table 1 lists the values of refractive index and mean density for three typical aerosol types calculated by the partial molar refractive approach.The mean densities for three aerosol types at the dry state range from 1.803 to 1.890 g/m 3 .The real parts of refractive index for urban, continental, and marine aerosols are 1.575, 1.557 and 1.479, respectively.As reviewed by Horvath [19], only black carbon (BC, the main constituent of soot) in atmospheric aerosol particles is highly absorbed.Hematite (a-Fe 2 O 3 ) is the only other substance having a light absorption comparable to EC in the near suggest to use full name of "UV", u. v., but absorption rapidly decreases in the visible spectrum of the light.There are some discrepancies about the value of the complex refractive index of EC because of the difficulty of its experimental determination.The values given in the literature range from 1.2 to 2.0 for the real part and from -0.1 to -1.0 for the complex part [19].
In this study, the refractive index used for EC is 2.0 -0.66i.Since the imaginary parts for all ions in Table 1 are zero and the densities of each ion in Table1 are not known, it is not easy to calculate the partial mole refractions of the ions for imaginary parts using the definition equation (5).In this study, the imaginary part of muticomponent aerosols is calculated using the volume average of the imaginary parts of refractive index of the individual species, i m , as follows [17]: where m i is the imaginary part of refractive index of component i.With the estimates of BC concentration for three types of aerosols in Table 1, it was found that the complex refractive indices for urban, continental and marine aerosols are 1.575 -0.027i, 1.557 -0.016i, 1.479 -.0027i, respectively.Hänel [10] found that the real part of refractive index for urban aerosols in the city of Mainz, Germany, was 1.57  0.04 by actual measurement.Grams et al. [20] determined that the complex re-fractive index for urban aerosols in the city of Boulder, Colorado O, was 1.55 -0.044i on the basis of light scattering measurements.The results from this study are very close to these actual measurements.These complex refractive indices for three types of aerosols will be used in the calculation hereafter.

The Sensitivity to Relative Humidity
A Mie theory computer code developed by Dave [21] is used in this study to compute aerosol radiative properties.
All aerosol particles are assumed to be spherical in shape in the calculation.Table 3 shows the values of the particle light scattering and extinction coefficients calculated with the above assumption at RHs of 30%, 80% and 99% for different particle size distributions of several aerosol types at a wavelength of 580 nm.The wavelength, 580 nm, is chosen based on the recommendation by Horvath [19] to give the maximum perception of an object under the daylight conditions.As shown, the growth factors for an RH range of 30 to 80% RH range from 1.57 to 1.92 (average 1.77 0.12) and from 1.55 to 1.90 (average 1.77  0.11) for scattering and extinction coefficients, respectively.This is in agreement with the criterion value of the hydroscopic growth factor (1.7 0.3)(which is defined as the ratio of the light scattering coefficient by an aerosol at an RH of 80% to that at 30%) derived from the direct nephelometer measurement [22].This value has been utilized to date as the first estimate in climate change modeling studies [1].It is interesting to note that Hegg et al. [23] obtained substantially larger values of the hygroscopic growth (see Table 1 of Hegg et al. [23]) for the same size distribution as those in Table 3. Hegg et al. [23] attributed it to be influenced by the position of the initial dry aerosol size distribution relative to the effective light scattering droplet size range.The main differences in our calculation results and those of Hegg et al. [23] lie in different values of the refractive index and mean linear mass increase coefficient used for aerosol particles.The consistence of our results in Table 3 with the range of hygroscopic growth factor (1.5 to 1.8) from the direct measurements of Charlson et al. [22] indicates that our calculation for the effects of RH on scattering coefficient is reasonable.At a high RH such as 99%, the growth factors are much higher and more variable than values at lower RHs as shown in Table 4.The growth factors range from 1.06 to 1.18 (average 1.12 0.04) and from 1.10 to 1.53 (average 1.32 0.13) for asymmetry factor in the RH range of 30% to 80% and 30% to 99%, respectively.The growth factors range from 1.01 to 1.06 (average 1.03 0.02) and from 1.02 to 1.14 (average 1.08 0.04) for the single scattering albedo in the RH range of 30% to 80% and 30% to 99%, respectively.The single scattering albedo is not sensitive to RH.At a high RH such as 99%, the single scatter albedo is close to 1.0.The single scattering albedo and asymmetry factor are insensitive to changes in RH.This is in agreement with those of Pilinis et al. [24].Both scattering and extinction coefficients are more sensitive to changes in RH than single scatter albedo and asymmetry factor.

The Sensitivity to Refractive Index
In the following sensitivity studies, the parameters used for three types of aerosols are assumed to be (1) urban aerosols of Meszaros [25], N=560 cmm, D g =0.100 m, g =2.0, m=1.590 -0.027i, RH = 80%; (2) continental aerosols of Hoppel et al. [24], N = 3000 cm -3 , D g = 0.080 m,  g = 2.0, m = 1.564 -0.016i, RH = 80%; (3) marine aerosols of Gathman [27], N = 67 cm -3 , D g =0.266 m,  g = 1.622, m = 1.479 -0.003i, RH = 80%.Note that the values of radius, refractive index in the above assumptions are for a dry state.RH is set to be 80% in the Mie calculation.Table 5 lists the ranges and averaged values of the change factors for the effects of real and imaginary parts of refractive index on the aerosol radiative properties.The scattering and extinction coefficients increase by about 48% and asymmetry factor decrease by 6% with real part increasing from 1.4 to 1.65.But the single scattering albedo is insensitive to the changes in real part.Figures 3(a) and (b) show extinction coefficient and single scatter albedo as a function of real part of refractive index for three types of aerosols at a wavelength of 580 nm.Table 5 shows that the scattering coefficient and single scattering albedo decrease by 18% and 24% when imaginary part varies from -0.005 to 0.10, respectively.The extinction coefficient and asymmetry factor are insensitive to the change in the imaginary part.As expected, extinction coefficient and asymmetry factor increase slightly as imaginary part increases.

The Sensitivity to Size Distributions
As shown in Table 5, scattering and extinction coefficients are very sensitive to changes in geometric mean radius.The scattering and extinction coefficients increase by factors of 118 and 123, respectively, whereas the asymmetry factor only increases by 17% and the single scattering albedo decreases by 0.8%, when the geometric mean radius varies from 0.05 to 0.3 m.Figures 4(a) and (b) show the sensitivity tests for the case of marine aerosols at different wavelengths.Table 5 lists the ranges and averaged changes of radiative properties for three types of aerosols when geometric standard deviaion ( g ) varies from 1.2 to 3.0.The scattering and t  show the changes of the shape of aerosol size distribution when geometric mean radius varies from 0.1 to 0.4 m at N 0 =560 cm -3 and  g = 2.0 and when geometric standard deviation varies from 1.2 to 3.0 at N 0 = 560 cm -3 and r g =0.15 m, respectively.Since the light scattering efficiency of an individual particle is dependent on the particle size, with peak efficiencies occurring between ~0.2 and 0.7 m in particle radius for a light wavelength of 580 nm, aerosol particles can have large scattering and extinction coefficients if their size distributions grow into this efficient light scattering size range.Figure 5 indicates that both cases can result in more particles in the efficient light scattering size range (with radii of 0.2 to 0.7 m).It is not surprised to find that the scattering and extinction coefficients are very sensitive to the changes in geometric mean radius and geometric standard deviation.

The Sensitivity of Wavelength Dependence of Radiative Properties
The wavelength dependence of aerosol radiative properties is very sensitive to geometric mean radius.When the geometric mean radius is small, both single scattering albedo and asymmetry factor decrease with increasing wavelengths, but when the geometric mean radius becomes larger than a value, both single scattering albedo and asymmetry factor increase with increasing wavelengths.For the latter case, the Angstrom law will not be applicable.The values of geometric mean radii at the crossing point are different for asymmetry factor and single scattering albedo as shown in Figures 4(a) and (b), and are also determined by the geometric standard deviation as analyzed below.Since the light scattering efficiency of an individual particle is a nonlinear function of particle size and depends on the particle size and light wavelength tested, and the refractive index is wavelength dependent, the wavelength dependence of aerosol radiative properties will strongly rely on the size distribution and refractive index.For the wavelength dependence of refractive index, available data were closely matched by setting n() = n( = 0.598 m) -0.03( -0.598),where is the wavelength in m.As shown, the wavelength dependence of refractive index is weak.As shown in Figure 4, the wavelength dependence of asymmetry factor and single scattering albedo strongly relies on the geometric mean radius and geometric standard deviation.But the wavelength dependence of scattering and extinction coefficients on the geometric mean radius and geo-metric standard deviation is weak.For small geometric mean radius and small geometric standard deviation, both asymmetry factor and single scattering albedo increase with decreasing wavelengths, however, for large values of geometric mean radius and geometric standard deviation, both asymmetry factor and single scattering albedo increase with increasing wavelengths, especially for single scattering albedo, as shown in Figure 4.

Radiation Transmission
Since human-induced aerosols are likely to greatly influence future regional climate change instead of global climate change, it is of interest to examine the sensitivity of the aerosol-induced radiation transmission changes at a local or regional scale to aerosol composition, size distributions, and RH.In this study, the radiation transmission is calculated for the assumed aerosol layer with a depth of 2 kilometers using the Madronich's Tropospheric Ultraviolet-Visible Radiation Transfer Model (TUVRTM) [28].The optical depth is      sults of aerosol radiative properties for the three types of aerosols.Table 6 lists the radiation transmissions at 580 nm for different aerosol types at RHs of 30%, 80% and 99%. Figure 6 shows the sensitivity of radiation transmission to RH, refraction index, number concentrations and size distributions for the three types of aerosols.Table 7 lists the change factors for radiation transmission for three types of aerosols.Note that the radiation transmission at 580 nm is 0.911 without the aerosol layer under the assumed atmospheric conditions.It is interesting to note that the radiation transmission is not sensitive to the changes in the above parameters if the total aerosol number concentration is small as it for maritime aerosols of Gathman [27] (total number concentration is only 67 cm -3 as indicated in Table 7).In this case, the radiation transmission only decreases by 0.4% and 0.5% when RH varies from 0% to 95% and the real part varies from 1.40 to 1.65, respectively.The radiation transmission is sensitive to the change in imaginary part and number concentrations with the decrease of visible radiation transmission by 2.7% and 4.2% when the imaginary part varies from -0.005 to -0.1 and number concentration from 50 to 4000 cm -3 , respectively.The radiation transmission is very sensitive to the changes in geometric mean radius and geometric standard deviation.The radiation transmission decreases by 76% when geometric mean radius varies from 0.05 to 0.3 m and decreases by 12% when geometric standard deviation varies from 1.2 to 3.0.This is in agreement with the strong dependence of scattering and extinction coefficients on geometric mean radius and geometric standard deviation.It should be emphasized that the radiation transmission also strongly depends on the solar zenith angle, latitude and longitude, and ozone concentrations.

Conclusions
In this work, the partial molar refraction method is used to accurately calculate the real part of refractive index of aerosol particles with actual measured chemical compositions including soluble inorganic and organic ions and insoluble inorganic and organic substances.It is found that the complex refractive indices for urban, continental and marine aerosols are 1.575 -0.027i, 1.557 -0.016i and 1.479 -0.003i, respectively.The scattering and extinction coefficients are sensitive to changes in RH, while both single scattering albedo and asymmetry factor are insensitive to change in RH.The extinction coefficient and asymmetry factor are sensitive to changes in real part of refractive index.The scattering coefficient and single scattering albedo are sensitive to the imaginary part changes.The aerosol radiative properties are very sensitive to the change in both geometric mean radius and geometric standard deviation of a particle size distribution.The radiation transmission decreases by 76% and 12% when geometric mean radius varies from 0.05 to 0.3 m and geometric standard deviation varies from 1.2 to 3.0, respectively.Other sensitivities for the radiation transmissions are insignificant.The comparison between theoretical calculation and actual measurement will be necessary in the future work.

Figure 2 .
Figure 2. Density, refractive index, and radius as a function of RH for three types of aerosols.

Figure 3 .
Figure 3.The radiative properties at 580 nm as a function of real and imaginary parts of refractive index for three types of aerosols at a dry state.

Figure 4 .Figure 5 .
Figure 4.The radiative properties at 580 nm as a function of geometric mean radius (for Gathma's maritime aerosols (a, b), and geometric standard deviation (for Meszaros' urban aerosols (c, d)).
a constant extinction coefficient within the aerosol layer.The sensitivity of aerosol-induced radiation transmission changes at 580 nm is examined under the following constant conditions: date = 7/01/1995, O 3 = 278 DU, ground albedo = 0.15, air pressure = 940 mb, Latitude = 35.63°,longitude = 82.33°,UT = 17.90, solar zenith angle=13.31,the aerosol layer = 2 km.Three aerosol radiative properties (optical depth, asymmetry factor, and single scattering albedo) are needed in the TUVRTM model to calculate the aerosol-induced radiation transmission changes.In this section, the sensitivity of the aerosol-induced radiation transmission change to RH, refractive index, and size distribution is studied based on previous calculation re-

Figure 6 .
Figure 6.The radiation transmission at 580 nm across an aerosol layer with a 2-km in depth as a function of RH, real and imaginary arts, number concentration, and size distribution for three types of aerosols.p

Table 7 .
The change factors for radiation transmission at 580 nm as a function of relative humidity and radiative properties for three types of aerosols.* The average is calculated only for urban and continental aerosols.